Good. The last Shogun was awarded a very high ranking title of Imperial nobility, lived quietly, did nothing to attempt to stir up dissent, basically did everything the Restoration state would have hoped for. Admittedly there was no real nostalgia for the Shogunate, so he would have had few opportunities to cause trouble even if he had wanted to. But the official story was that the last Shogun stood down because he knew it was the best thing for Japan to experience a "restoration" of Imperial authority, so it was entirely in keeping for the Emperor to acknowledge this and treat him like another faithful servant.

That being said I don't think they were personally that close. I presume they would have met at least once, when the Emperor granted the Shogun his title, but beyond that there are few records. Basically after abdicating the Shogun lived a life of comfortable obscurity, although some of his descendants became active in Japanese politics.